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Wolfram Language & System Documentation Center
ProbabilityScalePlot
  • See Also
    • QuantilePlot
    • ProbabilityPlot
    • EstimatedDistribution
    • CDF
    • SmoothKernelDistribution
  • Related Guides
    • Statistical Visualization
    • Reliability
    • Random Variables
    • See Also
      • QuantilePlot
      • ProbabilityPlot
      • EstimatedDistribution
      • CDF
      • SmoothKernelDistribution
    • Related Guides
      • Statistical Visualization
      • Reliability
      • Random Variables

ProbabilityScalePlot[{x1,x2,…}]

generates a normal probability plot of the samples xi.

ProbabilityScalePlot[{x1,x2,…},"dist"]

generates a probability plot scaled for the distribution "dist".

ProbabilityScalePlot[{data1,data2,…},"dist"]

generates several scaled probability plots for data1, data2, ….

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Tabular Data  
Presentation  
Options  
ClippingStyle  
ColorFunction  
ColorFunctionScaling  
Show More Show More
Filling  
FillingStyle  
GridLines  
GridLinesStyle  
Joined  
Mesh  
MeshFunctions  
MeshShading  
MeshStyle  
Method  
PlotHighlighting  
PlotLegends  
PlotMarkers  
PlotRange  
PlotStyle  
PlotTheme  
ReferenceLineStyle  
ScalingFunctions  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • QuantilePlot
    • ProbabilityPlot
    • EstimatedDistribution
    • CDF
    • SmoothKernelDistribution
  • Related Guides
    • Statistical Visualization
    • Reliability
    • Random Variables
    • See Also
      • QuantilePlot
      • ProbabilityPlot
      • EstimatedDistribution
      • CDF
      • SmoothKernelDistribution
    • Related Guides
      • Statistical Visualization
      • Reliability
      • Random Variables

ProbabilityScalePlot

ProbabilityScalePlot[{x1,x2,…}]

generates a normal probability plot of the samples xi.

ProbabilityScalePlot[{x1,x2,…},"dist"]

generates a probability plot scaled for the distribution "dist".

ProbabilityScalePlot[{data1,data2,…},"dist"]

generates several scaled probability plots for data1, data2, ….

Details and Options

  • ProbabilityScalePlot[data,"dist"] uses distribution-specific scales so that if data follows the given distribution, the plot will lie on a straight line.
  • The following distribution-specific scales are supported:
  • "Normal"normal plot
    "Weibull"Weibull plot
    "Exponential"exponential plot
    "LogNormal"lognormal plot
    "Rayleigh"Rayleigh plot
    "Frechet"Fréchet plot
    "Gumbel"Gumbel plot
  • The positions plotted correspond to {xi,yi} where yi are uniform order statistics medians given by Quantile[{x1,x2,…},].
  • The data is scaled by distribution-specific transformations and given by:
  • "Exponential"
    "Frechet"
    "Gumbel"
    "LogNormal"
    "Normal"
    "Rayleigh"
    "Weibull"
  • Datasets can be given in the following forms:
  • {x1,x2,…}list of samples
    {Quantity[x1,unit],Quantity[x2,unit],…}samples with units
    <|k1e1,k2e2,…|>association of keys and samples
    WeightedData[…],EventData[…]augmented datasets
    TimeSeries[…],EventSeries[…],TemporalData[…]time series, event series, and temporal data
    w[{e1,e2,…},…]wrapper applied to a whole dataset
    w[{data1,data2,…}]wrapper applied to all datasets
  • The form w[data] provides a wrapper w to be applied to the resulting graphics primitives.
  • ProbabilityScalePlot[Tabular[…]cspec] extracts and plots values from the tabular object using the column specification cspec.
  • The following forms of column specifications cspec are allowed for plotting tabular data:
  • colxplot the values from column x
    {colx1,colx2,…}plot columns x1, x2, …
  • The following wrappers can be used:
  • Annotation[e,label]provide an annotation
    Button[e,action]define an action to execute when the element is clicked
    EventHandler[e,…]define a general event handler for the element
    Highlighted[datai,effect]dynamically highlight fi with an effect
    Highlighted[datai,Placed[effect,pos]]statically highlight fi with an effect at position pos
    Hyperlink[e,uri]make the element act as a hyperlink
    PopupWindow[e,cont]attach a popup window to the element
    StatusArea[e,label]display in the status area when the element is moused over
    Style[e,opts]show the element using the specified styles
    Tooltip[e,label]attach an arbitrary tooltip to the element
  • ProbabilityScalePlot has the same options as Graphics, with the following additions and changes: [List of all options]
  • AspectRatio1/GoldenRatioratio of height to width
    ClippingStyle Automaticwhat to draw where curves are clipped
    ColorFunction Automatichow to determine the coloring of curves
    ColorFunctionScaling Truewhether to scale arguments to ColorFunction
    Filling Nonefilling to insert under each curve
    FillingStyle Automaticstyle to use for filling
    Joined Automaticwhether to join points
    Mesh Nonehow many mesh points to draw on each curve
    MeshFunctions {#1&}how to determine the placement of mesh points
    MeshShading Nonehow to shade regions between mesh points
    MeshStyle Automaticthe style for mesh points
    Method Automaticmethods to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotHighlighting Automatichighlighting effect for curves
    PlotLegends Nonelegends for data points
    PlotMarkers Nonemarkers to use to indicate each point for datasets
    PlotRange Automaticrange of values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotStyle Automaticgraphics directives to specify the style for each object
    PlotTheme $PlotThemeoverall theme for the plot
    ReferenceLineStyle Automaticstyle for the reference line
    ScalingFunctions Nonehow to scale individual coordinates
    WorkingPrecisionMachinePrecisionthe precision used in internal computations for symbolic distributions
  • With Filling->Automatic, the region between a dataset and reference line will be filled. By default "stems" are used for datasets and "solid" filling is used for symbolic distributions. The setting Joined->True will force "solid" filling for datasets.
  • The arguments supplied to functions in MeshFunctions and RegionFunction are , . Functions in ColorFunction are by default supplied with scaled versions of these arguments.
  • The setting PlotStyle->Automatic uses a sequence of different plot styles for different lines.
  • ColorData["DefaultPlotColors"] gives the default sequence of colors used by PlotStyle.
  • With the ReferenceLineStyle->None, no reference line will be drawn.
  • Possible highlighting effects for Highlighted and PlotHighlighting include:
  • stylehighlight the indicated data
    "Ball"highlight and label the indicated point in data
    "Dropline"highlight and label the indicated point in data with droplines to the axes
    "XSlice"highlight and label all points along a vertical slice
    "YSlice"highlight and label all points along a horizontal slice
    Placed[effect,pos]statically highlight the given position pos
  • Highlight position specifications pos include:
  • x, {x}effect at {x,y} with y chosen automatically
    {x,y}effect at {x,y}
    {pos1,pos2,…}multiple positions posi
  • Typical settings for PlotLegends include:
  • Noneno legend
    Automaticautomatically determine legend
    {lbl1,lbl2,…}use lbl1, lbl2, … as legend labels
    Placed[lspec,…]specify placement for legend
  • Possible settings for ScalingFunctions include:
  • syscale the y axis
    {sx,sy}scale x and y axes
  • Common built-in scaling functions s include:
  • "Reverse"reverse the coordinate direction
  • List of all options
  • Highlight options with settings specific to ProbabilityScalePlot
  • AlignmentPointCenterthe default point in the graphic to align with
    AspectRatio1/GoldenRatioratio of height to width
    AxesFalsewhether to draw axes
    AxesLabelNoneaxes labels
    AxesOriginAutomaticwhere axes should cross
    AxesStyle{}style specifications for the axes
    BackgroundNonebackground color for the plot
    BaselinePositionAutomatichow to align with a surrounding text baseline
    BaseStyle{}base style specifications for the graphic
    ClippingStyleAutomaticwhat to draw where curves are clipped
    ColorFunctionAutomatichow to determine the coloring of curves
    ColorFunctionScalingTruewhether to scale arguments to ColorFunction
    ContentSelectableAutomaticwhether to allow contents to be selected
    CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
    Epilog{}primitives rendered after the main plot
    FillingNonefilling to insert under each curve
    FillingStyleAutomaticstyle to use for filling
    FormatTypeTraditionalFormthe default format type for text
    FrameFalsewhether to put a frame around the plot
    FrameLabelNoneframe labels
    FrameStyle{}style specifications for the frame
    FrameTicksAutomaticframe ticks
    FrameTicksStyle{}style specifications for frame ticks
    GridLinesNonegrid lines to draw
    GridLinesStyle{}style specifications for grid lines
    ImageMargins0.the margins to leave around the graphic
    ImagePaddingAllwhat extra padding to allow for labels etc.
    ImageSizeAutomaticthe absolute size at which to render the graphic
    JoinedAutomaticwhether to join points
    LabelStyle{}style specifications for labels
    MeshNonehow many mesh points to draw on each curve
    MeshFunctions{#1&}how to determine the placement of mesh points
    MeshShadingNonehow to shade regions between mesh points
    MeshStyleAutomaticthe style for mesh points
    MethodAutomaticmethods to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotHighlightingAutomatichighlighting effect for curves
    PlotLabelNonean overall label for the plot
    PlotLegendsNonelegends for data points
    PlotMarkersNonemarkers to use to indicate each point for datasets
    PlotRangeAutomaticrange of values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotRangePaddingAutomatichow much to pad the range of values
    PlotRegionAutomaticthe final display region to be filled
    PlotStyleAutomaticgraphics directives to specify the style for each object
    PlotTheme$PlotThemeoverall theme for the plot
    PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
    Prolog{}primitives rendered before the main plot
    ReferenceLineStyleAutomaticstyle for the reference line
    RotateLabelTruewhether to rotate y labels on the frame
    ScalingFunctionsNonehow to scale individual coordinates
    TicksAutomaticaxes ticks
    TicksStyle{}style specifications for axes ticks
    WorkingPrecisionMachinePrecisionthe precision used in internal computations for symbolic distributions

Examples

open all close all

Basic Examples  (3)

A normal probability plot compared to an estimated normal distribution:

A Weibull probability plot:

Normal probability plot of several datasets with a legend:

Scope  (30)

Data  (13)

ProbabilityScalePlot works with numeric data:

ProbabilityScalePlot with multiple datasets:

Normal probability plot:

A Weibull probability plot:

An exponential probability plot:

Lognormal probability plot:

Rayleigh probability plot:

Fréchet probability plot:

Gumbel probability plot:

Plot values with units:

Plot the values from an association:

Plot data with weights:

Plot data from time series:

Tabular Data  (1)

Get tabular data:

Compare the data to a normal distribution:

Compare multiple sets of data:

Use PivotToColumns to generate columns of "SepalWidth" per species:

Compare probability of sepal width per species:

Use abbreviated names for extended keys when the elements are unique:

Use legends for the plot:

Presentation  (16)

Multiple datasets are automatically colored to be distinct:

Provide explicit styling to different sets:

Include legends for each dataset:

Use Legended to provide a legend for a specific dataset:

Add labels:

Use specific styles for the reference line:

Turn off the reference line:

Draw grid lines:

Provide an interactive Tooltip for the data:

Create filled plots:

Use shapes to distinguish different datasets:

Use Joined to connect datasets with lines:

Use a theme to create a black-and-white plot:

Reverse the direction of the x axis:

Plots usually have interactive callouts showing the coordinates when you mouse over them:

Including specific wrappers or interactions, such as tooltips, turns off the interactive features:

Choose from multiple interactive highlighting effects:

Options  (78)

ClippingStyle  (4)

Omit clipped regions of the plot:

Show the clipped regions like the rest of the curve:

Show the clipped regions with red lines:

Show the clipped regions as red and thick:

ColorFunction  (6)

ColorFunction requires at least one dataset to be Joined:

Color by scaled and coordinates:

Color with a named color scheme:

Fill to the reference line with the color used for the curve:

ColorFunction has higher priority than PlotStyle for coloring the curve:

Use Automatic in MeshShading to use ColorFunction:

ColorFunctionScaling  (2)

Color the line based on scaled value:

Color the line based on unscaled value:

Filling  (7)

Fill from data to the reference line:

Use symbolic or explicit values for filling:

Points fill with stems:

Curves fill with solid regions:

Fill from the third dataset to the bottom:

Fill between datasets using a particular style:

Use different styles above and below the filling level:

Filling only applies where the datasets overlap:

FillingStyle  (2)

Use different fill colors:

Fill with transparent orange regions:

GridLines  (1)

Use automatically computed grid lines:

GridLinesStyle  (1)

Use light gray grid lines:

Joined  (1)

Datasets are not joined by default:

Join the points:

Mesh  (4)

Use 20 mesh levels evenly spaced in the direction:

Use the mesh to divide the curve into deciles:

Use an explicit list of values for the mesh:

Specify mesh positions and styles:

MeshFunctions  (2)

Use a mesh evenly spaced in the and directions:

Show five mesh levels in the direction (red) and 10 in the direction (blue):

MeshShading  (6)

Alternate red and blue segments of equal width in the direction:

Use None to remove segments:

MeshShading can be used with PlotStyle:

MeshShading has higher priority than PlotStyle for styling the curve:

Use the PlotStyle for some segments by setting MeshShading to Automatic:

MeshShading can be used with ColorFunction:

MeshStyle  (4)

Color the mesh the same color as the plot:

Use a red mesh in the direction:

Use a red mesh in the direction and a blue mesh in the direction:

Use big red mesh points in the direction:

Method  (3)

By default a reference line is drawn through the first and third quartiles of data:

Draw the best-fit line through data:

The reference line represents the reference distribution:

PlotHighlighting  (9)

Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

Use PlotHighlightingNone to disable the highlighting for the entire plot:

Move the mouse over a set of points to highlight it using arbitrary graphics directives:

Move the mouse over the points to highlight them with balls and labels:

Move the mouse over the curve to highlight it with a label and droplines to the axes:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Use a component that shows the points on the plot closest to the position of the mouse cursor:

Specify the style for the points:

Use a component that shows the coordinates on the points closest to the mouse cursor:

Use Callout options to change the appearance of the label:

Combine components to create a custom effect:

PlotLegends  (7)

By default, no legends are used:

Generate a legend using labels:

Generate a legend using placeholders:

Legends use the same styles as the plot:

Use Placed to specify the legend placement:

Place the legend inside the plot:

Use LineLegend to change the legend appearance:

PlotMarkers  (7)

QuantilePlot normally uses distinct colors to distinguish different sets of data:

Automatically use colors and shapes to distinguish sets of data:

Use shapes only:

Change the size of the default plot markers:

Use arbitrary text for plot markers:

Use explicit graphics for plot markers:

Use the same symbol for all the sets of data:

Use plot markers:

PlotRange  (3)

PlotRange is automatically calculated:

Show the whole dataset:

Show the distribution for between 1 and 3 and between 90 and 99:

PlotStyle  (3)

Use different style directives:

By default different styles are chosen for multiple curves:

Explicitly specify the style for different curves:

PlotTheme  (1)

Use a theme to create a black-and-white plot:

Use a solid, light gray reference line:

ReferenceLineStyle  (3)

ReferenceLineStyle by default uses a Dotted form of PlotStyle:

Draw a red dotted reference line:

Draw a solid red reference line:

Use None to turn off the reference line:

ScalingFunctions  (2)

By default ProbabilityScalePlot uses an automatic scale on both of the axes:

Reverse the direction of the x axis:

Applications  (2)

A group of ecologists surveyed an island's bird species populations. For each species on the island, the number of individuals observed was recorded. Often LogNormalDistribution is used to model abundance of species:

It appears that a lognormal model is a reasonable choice:

Find the best-fitting LogNormalDistribution using a maximum likelihood estimation:

Normal probability plot for a time slice of a random process:

Properties & Relations  (8)

Compare data with different reference distributions:

Compare the quantiles of data with quantiles of a normal distribution:

Compare the CDF of the data with the CDF of a normal distribution:

BoxWhiskerChart and DistributionChart can be used to visualize the distribution of data:

SmoothHistogram and Histogram can be used to visualize the distribution of data:

DiscretePlot can be used to visualize discrete distributions:

Use ListPlot to see the data:

ProbabilityScalePlot ignores time stamps when input is a TimeSeries:

See Also

QuantilePlot  ProbabilityPlot  EstimatedDistribution  CDF  SmoothKernelDistribution

Related Guides

    ▪
  • Statistical Visualization
  • ▪
  • Reliability
  • ▪
  • Random Variables

History

Introduced in 2010 (8.0) | Updated in 2012 (9.0) ▪ 2014 (10.0) ▪ 2022 (13.1) ▪ 2023 (13.3) ▪ 2025 (14.2)

Wolfram Research (2010), ProbabilityScalePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ProbabilityScalePlot.html (updated 2025).

Text

Wolfram Research (2010), ProbabilityScalePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ProbabilityScalePlot.html (updated 2025).

CMS

Wolfram Language. 2010. "ProbabilityScalePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/ProbabilityScalePlot.html.

APA

Wolfram Language. (2010). ProbabilityScalePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ProbabilityScalePlot.html

BibTeX

@misc{reference.wolfram_2025_probabilityscaleplot, author="Wolfram Research", title="{ProbabilityScalePlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ProbabilityScalePlot.html}", note=[Accessed: 04-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_probabilityscaleplot, organization={Wolfram Research}, title={ProbabilityScalePlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ProbabilityScalePlot.html}, note=[Accessed: 04-February-2026]}

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